Finite Group Databasebeta

← #29733086

Subgroups — #29733086

Order 15616.

1102 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840482C211yesmaximal, characteristic
2C2×#16840100C211yesmaximal, characteristic, complemented
3C2×#16840018C211yesmaximal, characteristic, complemented
4#21447152C211yesmaximal, characteristic, complemented
5#21447015C211yesmaximal, characteristic, complemented
6#21446960C211yesmaximal, characteristic, complemented
7#21446827C211yesmaximal, characteristic, complemented
8#21446163C211yesmaximal, characteristic, complemented
9#21446132C211yesmaximal, characteristic, complemented
10#21446126C211yesmaximal, characteristic, complemented
11#21446117C211yesmaximal, characteristic
12#21446072C211yesmaximal, characteristic, complemented
13#21446016C211yesmaximal, characteristic, complemented
14#21445538C211yesmaximal, characteristic, complemented
15C61×#2417C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18#16840482—24no—
19#16840482—24no—
20C2×#14519777C2211yescharacteristic
21C2×#14519770—21no—
22C2×#14519770—21no—
23C2×#14519764—21no—
24C2×#14519756C2211yescharacteristic
25C2×#14519756C2211yescharacteristic
26C2×C4×Dic122C2211yescharacteristic
27C2×#14519742—21no—
28C2×#14519736C2211yescharacteristic
29C2×#14519736C2211yescharacteristic
30#16840100—24no—
31#16840018—24no—
32C2×#14519710C2211yescharacteristic
33C2×#14519708C2211yescharacteristic
34C2×#14519708C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×C22⋊#92418C2211yescharacteristic
43C2×C22⋊#92418C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C2×C22⋊Q8×C61C2211yescharacteristic
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic
55C22×C4⋊C4×C61C2211yescharacteristic
56C61×#398—21no—
57C61×#396—21no—
58C61×#391C2211yescharacteristic
59C61×#389C2211yescharacteristic
60C61×#386—21no—
61C61×#380—21no—
62C61×#380C2211yescharacteristic
63C22×Dic122—21no—
64C22×Dic122C2311yescharacteristic
65C2×#11758202—22no—
66C2×#11758202—22no—
67C2×#11758202—41no—
68C2×#11758194—22no—
69C2×#11758194—22no—
70C2×#11758194—41no—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75#14519777—22no—
76#14519777—22no—
77#14519770—28no—
78#14519770—28no—
79#14519764—28no—
80#14519756—22no—
81#14519756—22no—
82#14519756—22no—
83#14519756D414yes—
84C4×Dic122—22no—
85C4×Dic122—22no—
86#14519742—28no—
87#14519736—22no—
88#14519736—22no—
89#14519736—22no—
90#14519736D414yes—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×C22⋊Dic61—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61—21no—
105#14519710—22no—
106#14519708—22no—
107#14519708—22no—
108#14519701—22no—
109#14519701—22no—
110#14519701—22no—
111#14519700—22no—
112#14519700—22no—
113#14519700—41no—
114C22⋊#92418—22no—
115C22⋊#92418—22no—
116C22⋊#92418—41no—
117C22×Q8×C61C2311yescharacteristic
118C22×D4×C61D411yescharacteristic
119C23×C4×C61—21no—
120C23×C4×C61C2311yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C22⋊Q8×C61—22no—
123C22⋊Q8×C61—22no—
124C22⋊Q8×C61—22no—
125C22⋊Q8×C61—41no—
126C4×D4×C61—22no—
127C4×D4×C61—22no—
128C2×C4⋊C4×C61—22no—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—41no—
134C2×C4⋊C4×C61D411yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61D411yescharacteristic
142C2×C22⋊C4×C61D411yescharacteristic
143C2×C42×C61C2311yescharacteristic
144#95×C61—21no—
145#95×C61—21no—
146#95×C61—21no—
147#95×C61—21no—
148C24×C61C2×D411yescharacteristic
149C24×C61C2×D411yescharacteristic
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×D4×C61—22no—
157C2×D4×C61—22no—
158C2×D4×C61—41no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—42no—
174C22×C4×C61—42no—
175C22×C4×C61—81no—
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D412yes—
180C22×C4×C61C2×D412yes—
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2411yescharacteristic
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C2×Dic122—21no—
188C2×Dic122—21no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—24no—
192C2×Dic122—21no—
193C2×Dic122—42no—
194C2×Dic122—42no—
195C2×Dic122C2×D412yes—
196C4⋊C4×C61—22no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—42no—
203C4⋊C4×C61—42no—
204C4⋊C4×C61—42no—
205C4⋊C4×C61—81no—
206C4⋊C4×C61#4112yes—
207C22⋊C4×C61—22no—
208C22⋊C4×C61—22no—
209C22⋊C4×C61—42no—
210C22⋊C4×C61—42no—
211C22⋊C4×C61—81no—
212C42×C61—21no—
213C42×C61—21no—
214C22⋊Dic61—24no—
215C22⋊Dic61—24no—
216C22⋊Dic61—24no—
217C22⋊Dic61—24no—
218#11758202—44no—
219C4⋊Dic61—24no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61C2×D412yes—
224C4⋊Dic61C2×D412yes—
225C4⋊Dic61C2×D412yes—
226#11758196—24no—
227#11758196—24no—
228#11758196—24no—
229C4×Dic61—24no—
230C4×Dic61—24no—
231C4×Dic61—24no—
232#11758194—44no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418#4112yes—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61#12012yes—
259C23×C61C22×D411yescharacteristic
260Q8×C61—41no—
261Q8×C61—41no—
262Q8×C61—41no—
263Q8×C61—41no—
264D4×C61—44no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—22no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—84no—
296C2×C4×C61#12012yes—
297C2×C4×C61#13712yes—
298C2×C4×C61C22×D411yescharacteristic
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C2×#4111yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61H(5,𝔽2)11yescharacteristic
303C2×C4×C612−1+411yescharacteristic
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316Dic122—22no—
317Dic122—22no—
318Dic122—48no—
319Dic122—41no—
320Dic122—41no—
321#92418—22no—
322#92418—41no—
323#92418—41no—
324#92418—41no—
325#25558—611nomaximal, Sylow
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—22no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61C2×#12011yescharacteristic
341C22×C61#54611yescharacteristic
342C22×C61#54711yescharacteristic
343C22×C61C2×#13711yescharacteristic
344C22×C61#57511yescharacteristic
345C22×C61#57711yescharacteristic
346C22×C61#57811yescharacteristic
347C4×C61—22no—
348C4×C61—22no—
349C4×C61—41no—
350C4×C61—41no—
351C4×C61—42no—
352C4×C61—81no—
353C4×C61—81no—
354C4×C61—81no—
355C4×C61#53211yescharacteristic
356C4×C61#53711yescharacteristic
357C4×C61#54611yescharacteristic
358C4×C61#54711yescharacteristic
359Dic61—42no—
360Dic61—42no—
361Dic61—42no—
362Dic61—42no—
363C2×#556—611no—
364C2×#485—611no—
365C2×#470—611no—
366#2417D6111yescharacteristic
367#2058—611no—
368#2035—611no—
369#2024—611no—
370#2001—611no—
371#1878—611no—
372#1873—611no—
373#1872—611no—
374#1870—611no—
375#1863—611no—
376#1854—611no—
377#1736—611no—
378C2×C61—42no—
379C2×C61—81no—
380C2×C61#243011yescharacteristic
381C2×C61#300711yescharacteristic
382C2×C61#301311yescharacteristic
383C2×C61#331111yescharacteristic
384C2×C61#332811yescharacteristic
385C2×C61#334911yescharacteristic
386C2×C61#335611yescharacteristic
387C22×Q16—611no—
388C22×M16—611no—
389#556—1224no—
390#556—1224no—
391C2×C4⋊Q8—611no—
392C2×#126—1221no—
393C2×#126—1221no—
394C2×#124—1221no—
395C2×C22⋊Q8—611no—
396C2×C22⋊Q8—611no—
397C2×C22⋊Q8C2×D6111yescharacteristic
398C2×C22⋊Q8C2×D6111yescharacteristic
399C2×C4×Q8—611no—
400C2×C4×Q8—1221no—
401C2×C4×D4C2×D6111yescharacteristic
402C2×#117—611no—
403C2×#117—611no—
404C22×C4⋊C4C2×D6111yescharacteristic
405#485—1224no—
406#470—1224no—
407C2×#107—611no—
408C2×#106—611no—
409C2×#106—611no—
410C2×#103—611no—
411C2×#103—611no—
412C2×#103—611no—
413C2×#103—611no—
414C2×#103—611no—
415C2×#103—611no—
416C2×C22⋊C8—611no—
417C2×C22⋊C8—611no—
418C2×C22⋊C8—611no—
419#398—21no—
420#396—21no—
421#391C2×D6111yescharacteristic
422#389C2×D6111yescharacteristic
423#386—21no—
424#380—21no—
425#380C2×D6111yescharacteristic
426#340—611no—
427#340—611no—
428#340—611no—
429#340—611no—
430#340—611no—
431#340—611no—
432#336—611no—
433#336—611no—
434C61#2555811yescharacteristic, complemented, Sylow
435C22×Q8—611no—
436C22×Q8—1221no—
437C22×Q8C22×D6111yescharacteristic
438C22×D4C22⋊D6111yescharacteristic
439C23×C4—21no—
440C23×C4C22×D6111yescharacteristic
441C23×C4C22×D6111yescharacteristic
442C2×Q16—1222no—
443C2×Q16—1222no—
444C2×Q16—2441no—
445C2×M16—1222no—
446C2×M16—1222no—
447C2×M16—2441no—
448C22×C8—611no—
449C22×C8—611no—
450C22×C8—611no—
451C22×C8—611no—
452C4⋊Q8—1222no—
453C4⋊Q8—1222no—
454#126—1228no—
455#126—1228no—
456#124—1228no—
457C22⋊Q8—22no—
458C22⋊Q8—22no—
459C22⋊Q8—22no—
460C22⋊Q8—41no—
461C22⋊Q8—614no—
462C22⋊Q8—1222no—
463C22⋊Q8—1222no—
464C22⋊Q8—1222no—
465C4×Q8—1222no—
466C4×Q8—1222no—
467C4×Q8—1228no—
468C4×D4—22no—
469C4×D4—22no—
470#117—614no—
471#117—1222no—
472#117—1222no—
473#117—1222no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—41no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4C22⋊D6111yescharacteristic
488C2×C4⋊C4C22×D6111yescharacteristic
489C2×C4⋊C4C22×D6111yescharacteristic
490C2×C4⋊C4C22×D6111yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4C22⋊D6111yescharacteristic
499C2×C22⋊C4C22⋊D6111yescharacteristic
500C2×C42—1221no—
501C2×C42—1221no—
502C2×C42—1221no—
503C2×C42C22×D6111yescharacteristic
504#107—1222no—
505#106—1222no—
506#106—1222no—
507#103—1222no—
508#103—1222no—
509#103—1222no—
510#103—1222no—
511#103—1222no—
512#103—2441no—
513C22⋊C8—1222no—
514C22⋊C8—1222no—
515C22⋊C8—2441no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520C24C2×C22⋊D6111yescharacteristic
521C24C2×C22⋊D6111yescharacteristic
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—612no—
529C2×Q8—1224no—
530C2×Q8—1221no—
531C2×Q8—1221no—
532C2×Q8—1221no—
533C2×Q8—1221no—
534C2×Q8—1221no—
535C2×Q8—2442no—
536C2×Q8—2442no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—41no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—81no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4D4×D6112yes—
562C22×C4D4×D6112yes—
563C22×C4C2×C22⋊D6111yescharacteristic
564C22×C4C2×C22⋊D6111yescharacteristic
565C22×C4C2×C22⋊D6111yescharacteristic
566C22×C4C2×C22⋊D6111yescharacteristic
567C22×C4C23×D6111yescharacteristic
568Q16—2444no—
569M16—2444no—
570C2×C8—612no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C4⋊C4—21no—
583C4⋊C4—22no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—81no—
592C4⋊C4—612no—
593C4⋊C4—612no—
594C4⋊C4—612no—
595C4⋊C4—1224no—
596C4⋊C4—1224no—
597C4⋊C4—1224no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—1224no—
602C4⋊C4#1175822412yes—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—81no—
608C22⋊C4—1224no—
609C22⋊C4—1224no—
610C22⋊C4—1224no—
611C22⋊C4—1224no—
612C42—21no—
613C42—21no—
614C42—1224no—
615C42—1224no—
616C42—1224no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23#1451974512yes—
631C23C22×C22⋊D6111yescharacteristic
632Q8—41no—
633Q8—41no—
634Q8—41no—
635Q8—41no—
636Q8—1222no—
637Q8—1222no—
638Q8—2448no—
639Q8—2441no—
640Q8—2441no—
641D4—44no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—84no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4#1451974512yes—
686C2×C4#1451980812yes—
687C2×C4C2×D4×D6111yescharacteristic
688C2×C4C2×D4×D6111yescharacteristic
689C2×C4#41×D6111yescharacteristic
690C2×C4C2×#1175822411yescharacteristic
691C2×C4#1451982211yescharacteristic
692C2×C4#1451982411yescharacteristic
693C8—1222no—
694C8—2441no—
695C8—2441no—
696C8—2441no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22C2×#1451974511yescharacteristic
712C22#1684040611yescharacteristic
713C22#1684041111yescharacteristic
714C22C2×#1451980811yescharacteristic
715C22#1684056011yescharacteristic
716C22#1684057311yescharacteristic
717C22#1684057711yescharacteristic
718C4—22no—
719C4—22no—
720C4—41no—
721C4—42no—
722C4—41no—
723C4—81no—
724C4—81no—
725C4—81no—
726C4—2442no—
727C4—2442no—
728C4—2442no—
729C4—2442no—
730C4#1684030711yescharacteristic
731C4#1684033911yescharacteristic
732C4#1684040111yescharacteristic
733C4#1684041211yescharacteristic
734C2—42no—
735C2—81no—
736C2#2144942511yescharacteristic
737C2#2145507711yescharacteristic
738C2#2145513111yescharacteristic
739C2#2145785511yescharacteristic
740C2#2145810211yescharacteristic
741C2#2145834911yescharacteristic
742C2#2145843411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2417C2
socleC23×C61C22×D4
prime radicalC22×D4×C61D4
hypercenter#2417D61
hypocenterC61#25558
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2417

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#16840100C2semidirect
3. C2×#16840018C2semidirect
4. #21447152C2semidirect
5. #21447015C2semidirect
6. #21446960C2semidirect
7. #21446827C2semidirect
8. #21446163C2semidirect
9. #21446132C2semidirect
10. #21446126C2semidirect
12. #21446072C2semidirect
13. #21446016C2semidirect
14. #21445538C2semidirect
434. C61#25558semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168404822
C2×#168401002
C2×#168400182
#214471522
#214470152
#214469602
#214468272
#214461632
#214461322
#214461262
#214461172
#214460722
#214460162
#214455382
C61×#24172
#2555861